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Number of disconnected 3 X n binary matrices.
5

%I #10 Jun 13 2015 00:50:14

%S 0,1,11,102,882,7295,58533,459484,3547860,27043405,204016879,

%T 1526141666,11336059046,83703379691,614911337833,4497505562616,

%U 32769214114664,237956784843737,1722809101653651,12440161483566494,89616141395864986,644202131570116247

%N Number of disconnected 3 X n binary matrices.

%C A connected (0,1) matrix is one where you can get from any black square, i.e. 1, to any other by chess king moves.

%D R. Levy and J. Shapiro, Uniqueness in paint-by-numbers puzzles, preprint, 2000.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (14,-52,26,-35).

%F a(n) = 14*a(n-1)-52*a(n-2)+26*a(n-3)-35*a(n-4). G.f.: -x^2*(3*x-1) / ((7*x-1)*(5*x^3-3*x^2+7*x-1)). - _Colin Barker_, Jan 13 2014

%o (PARI) Vec(-x^2*(3*x-1)/((7*x-1)*(5*x^3-3*x^2+7*x-1)) + O(x^100)) \\ _Colin Barker_, Jan 13 2014

%Y Cf. A054417-A054420. 4*A054421(n) + 2*A054419(n) + A054420(n) = 7^n.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, May 22 2000

%E More terms from _James A. Sellers_, May 23 2000

%E More terms from _Colin Barker_, Jan 13 2014